41a2e9af19
This PR makes functions defined by well-founded recursion use an `opaque` well-founded proof by default. This reliably prevents kernel reduction of such definitions and proofs, which tends to be prohibitively slow (fixes #2171), and which regularly causes hard-to-debug kernel type-checking failures. This changes renders `unseal` ineffective for such definitions. To avoid the opaque proof, annotate the function definition with `@[semireducible]`.
60 lines
1.9 KiB
Text
60 lines
1.9 KiB
Text
open List MergeSort Internal
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-- If we omit the comparator, it is filled by the autoparam `fun a b => a ≤ b`
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example : mergeSort [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] = [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9] :=
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by native_decide
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example : mergeSort [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] (· ≤ ·) = [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9] :=
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by native_decide
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example : mergeSort [3, 100 + 1, 4, 100 + 1, 5, 100 + 9, 2, 10 + 6, 5, 10 + 3, 5] (fun x y => x/10 ≤ y/10) = [3, 4, 5, 2, 5, 5, 16, 13, 101, 101, 109] :=
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by native_decide
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example : mergeSortTR [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] = [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9] :=
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by native_decide
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example : mergeSortTR [3, 100 + 1, 4, 100 + 1, 5, 100 + 9, 2, 10 + 6, 5, 10 + 3, 5] (fun x y => x/10 ≤ y/10) = [3, 4, 5, 2, 5, 5, 16, 13, 101, 101, 109] :=
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by native_decide
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example : mergeSortTR₂ [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] = [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9] :=
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by native_decide
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example : mergeSortTR₂ [3, 100 + 1, 4, 100 + 1, 5, 100 + 9, 2, 10 + 6, 5, 10 + 3, 5] (fun x y => x/10 ≤ y/10) = [3, 4, 5, 2, 5, 5, 16, 13, 101, 101, 109] :=
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by native_decide
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/-!
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# Behaviour of mergeSort when the comparator is not provided, but typeclasses are missing.
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-/
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inductive NoLE
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| mk : NoLE
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/--
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error: could not synthesize default value for parameter 'le' using tactics
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---
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error: failed to synthesize
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LE NoLE
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Additional diagnostic information may be available using the `set_option diagnostics true` command.
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-/
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#guard_msgs in
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example : mergeSort [NoLE.mk] = [NoLE.mk] := sorry
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inductive UndecidableLE
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| mk : UndecidableLE
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instance : LE UndecidableLE where
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le := fun _ _ => true
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/--
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error: could not synthesize default value for parameter 'le' using tactics
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---
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error: type mismatch
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a ≤ b
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has type
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Prop : Type
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but is expected to have type
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Bool : Type
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-/
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#guard_msgs in
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example : mergeSort [UndecidableLE.mk] = [UndecidableLE.mk] := sorry
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